Use the properties of operations and rules for multiplying and dividing to solve (-3) divided by (3/4)x (2/7)x (-5/16) divide by (5/7)
To solve the expression (-3) divided by (3/4)x (2/7)x (-5/16) divide by (5/7), we can simplify each component step by step:
First, let's multiply the numerator and denominator of the fraction (3/4) by the whole number (-3):
(-3) divided by (3/4) becomes (-3)*(-4/3) = 12/3.
Next, let's multiply the resulting fraction (12/3) by the fraction (2/7):
(12/3) times (2/7) becomes (12*2)/(3*7) = 24/21.
Now, let's multiply the resulting fraction (24/21) by the fraction (-5/16):
(24/21) times (-5/16) becomes (24*(-5))/(21*16) = -120/336.
Finally, let's divide the resulting fraction (-120/336) by the fraction (5/7):
(-120/336) divided by (5/7) becomes (-120/336)*(7/5) = (-120*7)/(336*5) = -840/1680.
Now, we can simplify the fraction (-840/1680) by dividing both the numerator and denominator by their greatest common divisor, which is 840:
-840/1680 can be simplified to -1/2.
So, the solution to the expression (-3) divided by (3/4)x (2/7)x (-5/16) divide by (5/7) is -1/2.
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), we can simplify it step-by-step:
Step 1: Simplify the division (-3) ÷ (3/4):
To divide a number by a fraction, we multiply the number by the reciprocal of the fraction.
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Step 2: Simplify the multiplication -4 × (2/7):
To multiply fractions, we simply multiply the numerators and multiply the denominators.
-4 × (2/7) = (-4 * 2) / (1 * 7) = -8/7
Step 3: Simplify the multiplication -8/7 × (-5/16):
To multiply fractions, we multiply the numerators and multiply the denominators.
-8/7 × (-5/16) = (-8 * -5) / (7 * 16) = 40/112
Step 4: Simplify the division 40/112 ÷ (5/7):
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
40/112 ÷ (5/7) = 40/112 × (7/5) = (40 * 7) / (112 * 5) = 280/560
Step 5: Simplify the fraction 280/560:
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 280 and 560 is 280 (both numbers are divisible by 280).
280 ÷ 280 = 1
560 ÷ 280 = 2
So, 280/560 simplifies to 1/2.
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 1/2.
To solve the given expression, we'll follow the order of operations and use properties of operations. Here's the step-by-step solution:
Step 1: Start by applying the division operation "divided by" from left to right:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
Step 2: To divide by a fraction, we can multiply by its reciprocal. Therefore, we rewrite the expression as a multiplication problem:
(-3) × (4/3) × (2/7) × (-5/16) × (7/5)
Step 3: Next, let's simplify the expression by canceling out factors whenever possible:
(-3) × (4/3) × (2/7) × (-5/16) × (7/5)
= -3 × 4 × 2 × (-5) ÷ 3 × 7 × 16 × 5
= -3 × 4 × 2 × (-5) ÷ (3 × 7 × 16 × 5)
= -3 × 4 × (-5) ÷ (3 × 7 × 16 × 5)
= -3 × 4 × (-1) ÷ (16)
= -12 × (-1) ÷ 16
= 12 ÷ 16
= 3/4
Step 4: Simplify the expression further:
3/4 is already in simplest form. Therefore, the solution to the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) is 3/4.
So, the answer to the expression is 3/4.